We introduce a positivity-preserving numerical scheme for a class of nonlinear stochastic heat equations driven by a purely time-dependent Brownian motion. The construction is inspired by a recent preprint by the authors where one-dimensional equations driven by space-time white noise are considered. The objective of this paper is to illustrate the properties of the proposed integrators in a different framework, by numerical experiments and by giving convergence results.

翻译：针对一类由纯时间依赖布朗运动驱动的非线性随机热方程，我们提出了一种保正数值格式。该构造受作者近期预印本中关于由时空白噪声驱动的一维方程研究的启发。本文旨在通过数值实验和收敛性分析，阐述所提出的积分器在不同框架下的性质。